Problem: The equation of a circle $C$ is $x^2+y^2+10x-12y+45 = 0$. What is its center $(h, k)$ and its radius $r$ ?
Explanation: To find the equation in standard form, complete the square. $(x^2+10x) + (y^2-12y) = -45$ $(x^2+10x+25) + (y^2-12y+36) = -45 + 25 + 36$ $(x+5)^{2} + (y-6)^{2} = 16 = 4^2$ Thus, $(h, k) = (-5, 6)$ and $r = 4$.